The task of sampling and recovery is one of the most critical topics in the signal processing community. With the explosive growth of information and communication, signals
are being generated at an unprecedented rate from various sources,
including social networks, citation networks, biological networks,
and physical infrastructure [1]}, [2]}. Unlike time-series signals or images, these signals possess complex, irregular
structure, which requires novel processing techniques leading to the emerging field of signal processing on graphs [3]}, [4]}. Since the structure can be represented by a graph, we call these signals as graph signals. The interest in sampling and recovery of graph signals has increased in the last few years [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. Previous works have however studied sampling strategies on the entire graph in question which can often be expensive both in terms of computational and sample complexity. In this work, we present a structured sampling and recovery framework on product graphs. Product graphs are graphs that are composed of smaller graph atoms; we motivate how this model is a flexible and useful way to model richer data that may be multi-modal in nature [12]}, [4]}.
